Of those women who are diagnosed to have early-stage breast cancer, one-third eventually die of the disease. Suppose a screening program for the early detection of breast cancer was started in order to increase the survival rate \( p \) of those diagnosed to have the disease. A random sample of 200 women was selected from among those who were screened by the program and who were diagnosed to have the disease. Let \( X \) represent the number of those in the sample who survive the disease.### (a) Alternative HypothesisIf you wish to determine whether the community screening program has been effective, state the alternative hypothesis that should be tested.- \( H_a: p > \frac{2}{3} \)- \( H_a: p = \frac{2}{3} \)- \( H_a: p < \frac{2}{3} \)- \( H_a: p \neq \frac{2}{3} \)### (b) Null HypothesisState the null hypothesis.- \( H_0: p < \frac{2}{3} \)- \( H_0: p = \frac{2}{3} \)- \( H_0: p > \frac{2}{3} \)- \( H_0: p \neq \frac{2}{3} \)### (c) Test Statistic and ConclusionIf 194 women in the sample of 200 survive the disease, can you conclude that the community screening program was effective? Test using \( \alpha = 0.05 \).Find the test statistic and the rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)- Test statistic: \( z = \_\_\_\_ \)- Rejection region: \( z < \_\_\_\_ \), \( z > \_\_\_\_ \)State your conclusion and explain the practical conclusions from your test.- \( H_0 \) is rejected. There is sufficient evidence to indicate that \( p \) is greater than \(\frac{2}{3}\). The screening program seems to increase the survival rate.- \( H_0 \) is rejected. There is insufficient evidence to indicate that \( p \) is greater than \(\frac{2}{3}\). The screening program does not seem to increase the survival rate.- \( H_0 \

We have to conduct right tailed test for proportion.

Of those women who are diagnosed to have earlystage breast cancer, one-third eventually die of the disease. Suppose a screening program for the early detection of breast cancer was started in order to increase the survival rate p of those diagnosed to have the disease. A random sample of 200 women was selected from among those who were screened by the program and who were diagnosed to have the disease. Let x represent the number of those in the sample who survive the disease. A USE SALT (a) If you wish to determine whether the community screening program has been effective, state the alternative hypothesis that should be tested. (b) State the null hypothesis. O Moi p O Moi p (c) If 194 women in the sample of 200 survive the disease, can you conclude that the community screening program was effective? Test using a- 0.05. Find the test statistic and the rejection region. (Round your ansers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) test statistic rejection region State your conelusion and explain the practical conclusions from your test. H, is rejected. There is sufficient evidence to indicate that p is greater than The screening program seems to increase the survival rate. O Ho is rejected. There is insufficient evidence to indicate that p is greater than The screening program does not seem to increase the survival rate- O Hg is not rejected. There is sufficient evidence to indicate that p is greater than The screening program seems to increase the survival rate. O Hn is not rejected. There is insufficient evidence to indicate that p is greater than The screening program does not seem to increase the survival rate. (d) Find the prvalue for the test. (Round your answer to four decimal places.) pvalue - Interpret the pvalue. O Since the p-value is greater than 0.10. the results are not statistically significant. O Since the p-value is between 0.05 and 0.10, the results are tending toward statistical significance. O Since the p-value is between 0.01 and 0.05, the results are statistically significant. O Since the p-value is less than 0.01, the results are highly significant.